Absolute continuity of Bernoulli convolutions for algebraic parameters-Reference-Cited by-同舟云学术

Absolute continuity of Bernoulli convolutions for algebraic parameters

Published:2019-01-22 Issue:2 Volume:32 Page:351-397
ISSN:0894-0347
Container-title:Journal of the American Mathematical Society
language:en
Short-container-title:J. Amer. Math. Soc.

Author:

Varjú Péter

Abstract

We prove that Bernoulli convolutions μ λ \mu _\lambda are absolutely continuous provided the parameter λ \lambda is an algebraic number sufficiently close to 1 1 depending on the Mahler measure of λ \lambda .

Funder

Royal Society

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/jams/2019-32-02/S0894-0347-2019-00916-1/jams916_AM.pdf

Reference26 articles.

1. New Mathematical Monographs;Bombieri, Enrico,2006

2. The discretized sum-product and projection theorems;Bourgain, Jean;J. Anal. Math.,2010

3. On the dimension of Bernoulli convolutions, to appear in Ann. Probab.; arXiv:1610.09154v2;Breuillard, E.

4. Entropy of Bernoulli convolutions and uniform exponential growth for linear groups, to appear in J. Anal. Math.; arXiv:1510.04043v3;Breuillard, Emmanuel

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